Given a matrix A, a symmetrizer for A is a symmetric matrix Q such that QA is symmetric. The symmetrizer is a useful tool to obtain a-priori estimates for the solutions to hyperbolic equations. If Q is not positive definite, it is more convenient to consider a quasi-symmetrizer: a sequence of symmetric and positive defined matrices {Qε}ε∈]0,1] such that QεA approaches a symmetric matrix. In these notes we make a short survey of the basic notions of symmetrizer and quasi-symmetrizer and we give some applications to the well-posedness for the hyperbolic Cauchy problem.

Quasi-symmetrizer and hyperbolic equations

Giovanni Taglialatela
2013-01-01

Abstract

Given a matrix A, a symmetrizer for A is a symmetric matrix Q such that QA is symmetric. The symmetrizer is a useful tool to obtain a-priori estimates for the solutions to hyperbolic equations. If Q is not positive definite, it is more convenient to consider a quasi-symmetrizer: a sequence of symmetric and positive defined matrices {Qε}ε∈]0,1] such that QεA approaches a symmetric matrix. In these notes we make a short survey of the basic notions of symmetrizer and quasi-symmetrizer and we give some applications to the well-posedness for the hyperbolic Cauchy problem.
2013
978-3-319-00124-1
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/69938
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